Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are […]
Inspired by the categorification program for a numerical invariant of three-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the […]
CCMS Colloquium invites you to a talk by Ryan Moruzzi (CSU Northridge) Title: Exploring Leaky Forcing Through Hopi Rectangle graphs Abstract: Leaky forcing, introduced in 2019, is a graph-coloring process motivated by questions of network monitoring, in which the loss of information can hinder propagation through a graph. As a variant of standard zero forcing, […]
Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale […]
Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some […]
CCMS Colloquium invites you to a talk by Manuel Reyes (UCI) Title: When XY is not equal to YX Abstract: The commutative property of algebra states that the order of multiplication makes no difference: XY = YX. This property is so ingrained in our experience that it becomes difficult to imagine how algebra would function without it! If the commutative property fails, […]
Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will […]
One of the key objects used in Ngo's proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we'll discuss forthcoming work, […]
CCMS Colloquium invites you to a talk by Andrew Fiss (Michigan Technological University) Title: “Singing American Math: College Traditions from Book Burnings to Observatory Parties, 1880s-1920s" Abstract: “Singing Math” is a practice that linked American colleges of the late nineteenth and early twentieth centuries. A part of broader college singing traditions, it stood apart because of its […]
Abstract: Consider n independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a head and a tail, or flipped all coins. The Unanimous Vote problem asks us to find the ordering that minimizes […]
Many aggregation problems ask us to turn individual judgments into a single collective outcome. In this talk, we model each voter’s input as a relation on a set of alternatives, […]
Topology, akin to geometry, delves into the study of the shapes and structures of mathematical spaces, ranging from simple surfaces to intricate collections of functions and objects. In recent years, […]
